Composition

The Green Council was mostly formed of the members of King Viserys I's Small Council at the time of his death - which had come to be dominated by the Greens, the court faction of Viserys I's second wife, Queen Alicent Hightower. Of the seven men on that Small Council, only one was still openly loyal to Rhaenyra: Lyman Beesbury, the old Master of Coin who had served at court for many years and was determined to honor Viserys I's direct orders that Rhaenyra would succeed him to the throne. At the emergency Small Council meeting called upon Viserys I's death in his sleep, Beesbury alone refused to acquiesce to Aegon II usurping the throne - upon which Criston Cole promptly snuck up behind him and slit his throat. As Beesbury's warm blood still pooled across the table, the "Green council" was formed of the remaining six members, plus Queen Alicent as an advisor.

Aegon II's Small Council were his own immediate advisors at court, not necessarily all of the major leaders of "the Greens" during the civil war, i.e. Borros Baratheon wasn't a member of the council but continued to rule at Storm's End while contributing House Baratheon's armies to the war.

After the Blacks captured Harrenhal and Rhaenyra's assassins killed Aegon II's eldest son and heir, he grew impatient with his grandfather Otto's diplomatic maneuverings. Aegon II therefore ripped the chain of office from Otto's neck and replaced him as Hand of the King with Criston Cole himself.

Cole and Aegon II then marched to attack Black castles in the Crownlands, where at the Battle of Rook's Rest Aegon II was left crippled and heavily medicated into unconsciousness. Aegon II's younger brother Aemond Targaryen then served as Regent, joining Cole and the main Green army from King's Landing in a march north to Harrenhal. This turned out to be a trick to lure the capital city's defenders away, however, and Rhaenyra's forces from Dragonstone in the east quickly captured King's Landing. Aemond and Cole later died in battle, while the other members of the Green council were captured - but Aegon II escaped.

In the books

Tyland Lannister was originally Master of Ships at the time that Viserys I died; he was made the new Master of Coin to replace the murdered Lyman Beesbury. The Green council planned to offer the now-vacant position of Master of Ships to Lord Dalton Greyjoy of the Iron Islands to woo him into joining their side in the war. Dalton, however, didn't see much profit in sailing all the way around Westeros to raid Dragonstone and the Vale, while the wealth of Oldtown and Lannisport was both closer and more vulnerable on the western coasts, so he sided with the Blacks.

It is stated that as a result, the Blacks always had the advantage at sea during the civil war, possessing the Royal Fleet and Velaryon fleets in the east and the Iron Fleet in the west. The Greens did have the Redwyne fleet but it was reduced to a defensive posture around Oldtown against the ironborn. Ultimately the Greens had to ally with the Free Cities that hated Daemon to field any fleet against the Blacks. Given that the Greens never really controlled a significant number of ships, they apparently never bothered to appoint a new Master of Ships.

Ultimately, after Rhaenyra captured King's Landing she had Otto Hightower and Ironrod executed for treason, but kept Queen Mother Alicent alive and imprisoned. Criston Cole died soon afterwards in battle at the Butcher's Ball.

Tyland Lannister was also captured, but was kept alive - because he knew where the old royal treasury had been hidden, and the Blacks wanted to torture the information out of him. Tyland was blinded, gelded, and mutilated, but survived and was later freed when Aegon II retook the city about seven months later. Despite his grievous injuries he surprisingly turned out to still be an effective advisor and was restored to his position as Master of Coin. Grand Maester Orwyle was also taken prisoner, but his life was spared - for some time, at least. He wrote a major account of the war while in his cell, trying to make it slanted in Rhaenyra's favor so they would spare his life, and this was a major basis for Munkun's history of the Dance. It is unclear what ultimately happened to him. Larys Strong, meanwhile, escaped the city along with the then-comatose Aegon II and remained his greatest advisor up until the very end of the war.